Average Calculator

Calculate arithmetic mean, median, mode, range, geometric mean, harmonic mean, and sample or population standard deviation for any dataset.

Category: Math

How to Use Average Calculator

  1. Enter or paste your list of numbers separated by commas, spaces, semicolons, or line breaks.
  2. Review real-time statistical metrics including Arithmetic Mean, Median, Mode, Sum, Count, Min, Max, and Range.
  3. Compare Sample Standard Deviation (s, N−1) vs Population Standard Deviation (σ, N), Variance, Geometric Mean, and Harmonic Mean, then click Copy Summary Report.

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Frequently Asked Questions

What is the difference between Mean, Median, and Mode?

The Arithmetic Mean is the sum of all values divided by the total count (Σx / N). The Median is the middle number when the dataset is sorted in ascending order (or the average of the two middle numbers when N is even), making it resistant to extreme outliers. The Mode is the value that appears most frequently in the dataset.

When should I use Sample Standard Deviation (s) vs Population Standard Deviation (σ)?

Use Sample Standard Deviation (s, which divides the sum of squared deviations by N − 1 using Bessel's correction) when your numbers represent a sample drawn from a larger population. Use Population Standard Deviation (σ, which divides by N) when your dataset contains every member of the entire population being studied.

What are Geometric Mean and Harmonic Mean used for?

The Geometric Mean (the N-th root of the product of N positive numbers) is ideal for compounding growth rates, investment returns, and normalized ratios. The Harmonic Mean (N divided by the sum of reciprocals, N / Σ(1/x)) is used for averaging rates and speeds over equal distances. Both require all numbers in the dataset to be strictly positive (> 0).

How does the calculator handle non-numeric text or typos in my dataset?

You can separate numbers with commas, spaces, semicolons, or line breaks. If any token cannot be parsed as a valid finite number, the calculator immediately alerts you to the invalid entry so typos never silently skew your statistical average.

How is the Median calculated when there is an even number of values?

When the count N is odd, the median is the exact middle element at index (N + 1) / 2 of the sorted list. When N is even, there is no single middle element, so the calculator takes the arithmetic mean of the two central values at positions N/2 and (N/2) + 1.